Mr Byrne wants a legislation change to allow a policy where "for every white officer we recruit one black officer".

The Home Office said there was "no need for positive discrimination".

Cheshire Police last year introduced an outreach programme to attract female, LGBT and ethnic minority recruits.

But the chief constable admitted "the pace of change is still small" and suggested a change in the law could "speed things up" in terms of forces truly representing the communities they serve.

Asked whether he wanted to introduce positive discrimination, Mr Byrne said police forces should be able to emulate what happened in Northern Ireland when the Royal Ulster Constabulary (RUC) was renamed as the Police Service of Northern Ireland (PSNI) in 2001.

Because 90% of the RUC's officers were from a Protestant background, many Catholics in Northern Ireland believed the police did not represent them.

To tackle this, a 50-50 recruitment procedure, aimed at increasing the number of Catholic officers, was introduced and implemented until 2011.

'Might sound crazy'

Mr Byrne told the BBC the law should be changed in England "for a certain period of time" in order to allow forces to recruit more minority candidates.

"I've even taken legal advice about breaking the law," he said, "which might sound crazy as a senior police officer.

"But if we're put under pressure to change, then what are the consequences, other than reputational, from [breaking the law]?"

In response, a Home Office spokesman said forces were making "real progress" on diversity but dismissed the case for positive discrimination.

"To introduce such action would not only erode the credibility and confidence of individual officers, it would also undermine the public's expectation that progression in the police is based on merit alone."

Current equality law means employers cannot employ a job applicant because of characteristics such as race, sexual orientation or gender if other applicants are "better qualified".

Mr Byrne insisted: "We are not going to be lowering our standards.

"In Cheshire our officers have to go through a rigorous process to ensure they are fit to serve our community.

"It is the current employment law which is making it an almost impossible ambition for us to meet."

How diverse is Cheshire and its police force?

Chief Constable Simon Byrne says a lack of diversity amongst Cheshire's population means the force is "fishing in a small pond" for potential recruits.